On Pretopological Vector Spaces
Journal Title: Earthline Journal of Mathematical Sciences - Year 2019, Vol 1, Issue 2
Abstract
The purpose of the present paper is to introduce the new class of topological spaces, namely pretopological vector spaces. We study some of the basic properties of pretopological vector spaces and investigate their relationships with certain existing spaces. Along with other results, it is proved that translation of an open (resp. closed) set in a pretopological vector space is pre-open (resp. pre-closed), that translations (x \mapsto a+x) and dilations (x \mapsto \lambda x) on pretopological vector spaces are precontinuous.
Authors and Affiliations
Madhu Ram, Shallu Sharma
Keywords
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